Weighted sensitivity design of PID controllers for time-delay systems with a Smith predictor

Time delays in the feedback loop complicate the analysis and design of a controller system. The use of a Smith predictor in combination with a proportional integral derivative (PID) controller is a well-known technique for dealing with delays in stable systems. In this paper, a graphical method is introduced for finding all stabilizing PID controllers that satisfy a weighted sensitivity constraint of any arbitrary-order transfer function with time delay when the Smith predictor is used. Use of the Smith predictor tends to increase the size of the set of all PID controllers that satisfy the weighted sensitivity constraint in the controller parameter space. A numerical example is used to compare the set of PID controllers with and without a Smith predictor. A key advantage of this approach is that it requires only the frequency response of the plant.